Auditing Differential Privacy in High Dimensions with the Kernel Quantum Rényi Divergence
This work addresses the problem of verifying differential privacy for practitioners in machine learning and data science, offering a novel method for a known bottleneck in high-dimensional settings.
The authors tackled the challenge of auditing black-box differential privacy algorithms in high dimensions by proposing relaxations based on new divergences, specifically the kernel Rényi divergence and its regularized version, which can be estimated from samples to certify various DP guarantees.
Differential privacy (DP) is the de facto standard for private data release and private machine learning. Auditing black-box DP algorithms and mechanisms to certify whether they satisfy a certain DP guarantee is challenging, especially in high dimension. We propose relaxations of differential privacy based on new divergences on probability distributions: the kernel Rényi divergence and its regularized version. We show that the regularized kernel Rényi divergence can be estimated from samples even in high dimensions, giving rise to auditing procedures for $\varepsilon$-DP, $(\varepsilon,δ)$-DP and $(α,\varepsilon)$-Rényi DP.